Quantized fracture mechanics

Abstract

A new energy-based theory, quantized fracture mechanics (QFM), is presented that modifies continuum-based fracture mechanics; stress- and strain-based QFM analogs are also proposed. The differentials in Griffith's criterion are substituted with finite differences; the implications are remarkable. Fracture of tiny systems with a given geometry and type of loading occurs at ‘quantized’ stresses that are well predicted by QFM: strengths predicted by QFM are compared with experimental results on carbon nanotubes, β-SiC nanorods, α-Si₃N₄ whiskers, and polysilicon thin films; and also with molecular mechanics/dynamics simulation of fracture of carbon nanotubes and graphene with cracks and holes, and statistical mechanics-based simulations on fracture of two-dimensional spring networks. QFM is self-consistent, agreeing to first-order with linear elastic fracture mechanics (LEFM), and to second-order with non-linear fracture mechanics (NLFM). For vanishing crack length QFM predicts a finite ideal strength in agreement with Orowan's prediction. In contrast to LEFM, QFM has no restrictions on treating defect size and shape. The different fracture Modes (opening I, sliding II and tearing III), and the stability of the fracture propagations, are treated in a simple way.

Acknowledgements

The authors would like to thank S. Mielke, S. Zhang, D. Troya, G. Schatz, T. Belytschko, J. Achenbach, J. Weertman, B. Crist, A. Carpinteri and P. Cornetti, for many insightful discussions and A. L. Ruoff for critically reading and commenting on the manuscript prior to submission. RSR appreciates support from the NSF grant no. 0200797 “Mechanics of Nanoropes” (Ken Chong and Oscar Dillon, program managers), from the Office of Naval Research grant no. N00014-02-1-0870 “Mechanics of Nanostructures” (Mark Spector and John Pazik, program managers) and from the NASA University Research, Engineering and Technology Institute on Bio Inspired Materials (BIMat) under award No. NCC-1-02037 (Jeff Jordan, program manager).

Notes

Author for correspondence. Email: [email protected]

Additional information

Notes on contributors

Rodney S. Ruoff ‡

Author for correspondence. Email: [email protected]